{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "46a9c724",
   "metadata": {},
   "source": [
    "# 导数与微分\n",
    "\n",
    "## 导数\n",
    "\n",
    "导数是函数在某一点的变化率，用符号 $f'(x)$ 表示。导数的定义为：\n",
    "\n",
    "$$f'(x_0) = \\lim_{\\Delta x\\to 0} \\frac{f(x_0+\\Delta x)-f(x)}{\\Delta x}$$\n",
    "\n",
    "其中，$\\Delta x$ 是某个足够小的正数，称为微小变化量。导数的计算方法是用函数在某一点的切线斜率来近似表示函数在该点的变化率。\n",
    "\n",
    "<div style = \"text-align:center; padding: 10px; border-radius: 10px;\">\n",
    "\t<img src='..\\..\\public\\study\\导数.webp' styles=\"width: 100%; height: 100%;\">\n",
    "</div>\n",
    "\n",
    "$$f'(x) = \\frac{d}{dx}f(x) = \\lim_{h\\to 0} \\frac{f(x+h)-f(x)}{h}$$\n",
    "\n",
    "## 导数的几何意义\n",
    "\n",
    "导数的几何意义是函数在某一点的切线斜率。导数的大小表示函数在该点的变化率，而斜率的大小表示函数在该点的曲率。\n",
    "\n",
    "## 导数的求法\n",
    "\n",
    "导数的求法有多种方法。以下介绍几种常用的求导法则。\n",
    "\n",
    "### 泰勒公式\n",
    "\n",
    "泰勒公式是利用函数在某一点的切线来近似表示函数在该点的变化率的一种方法。泰勒公式的基本形式为：\t\n",
    "\n",
    "$$f(x) = f(a) + \\frac{f'(a)}{1!}(x-a) + \\frac{f''(a)}{2!}(x-a)^2 + \\frac{f'''(a)}{3!}(x-a)^3 + \\cdots$$\n",
    "\n",
    "其中，$a$ 是函数的某一点，$f'(a)$ 是 $f$ 在 $a$ 点的导数。泰勒公式的优点是计算简单，缺点是近似的程度受到 $h$ 的限制。\n",
    "\n",
    "### 利用导数的定义\n",
    "\n",
    "利用导数的定义，可以直接计算导数。\n",
    "\n",
    "### 利用微分定理\n",
    "\n",
    "微分定理是指函数在某一点的切线与该点连成的曲线的斜率等于函数在该点的导数。利用微分定理可以直接计算导数。\n",
    "\n",
    "### 利用求导法则\n",
    "\n",
    "求导法则是指利用导数的定义或微分定理来计算导数的一种方法。求导法则包括：\n",
    "\n",
    "- 链式法则：$f(g(x))' = f'(g(x))g'(x)$\n",
    "- 泰勒展开求导法则：$f(x+h) \\approx f(x) + f'(x)h + \\frac{1}{2}f''(x)h^2 + \\frac{1}{6}f'''(x)h^3 + \\cdots$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e205d31e",
   "metadata": {},
   "source": [
    "## 微分\n",
    "\n",
    "微分是一个变量在某个变化过程中的改变量的线性主要部分。若函数$y=f(x)$在点x处有导数$f'(x)$存在，则称函数$y=f(x)$在点x处可微，记作$dy=df(x)=f'(x)dx$。\n",
    "\n",
    "微分的中心思想是无穷分割。微分是函数改变量的线性主要部分。微积分的基本概念之一。\n",
    "\n",
    "## 导数与微分的关系\n",
    "\n",
    "导数也可以用微分来表示。\n",
    "$$f'(x) = \\frac{d}{dx}f(x)$$\n",
    "$$df(x)=f'(x)dx$$\n",
    "\n",
    "## 常用微分公式\n",
    "\n",
    "### 加法公式\n",
    "\n",
    "$$ d(f(x) + g(x)) = df(x) + dg(x)$$\n",
    "\n",
    "### 乘法公式\n",
    "\n",
    "$$ d(f(x)g(x)) = f(x)dg(x) + g(x)df(x)$$\n",
    "\n",
    "### 常量\n",
    "\n",
    "$$ d(c) = 0$$\n",
    "\n",
    "### 链式法则\n",
    "\n",
    "$$ d(f(g(x))) = f'(g(x))g'(x) + f(g(x))dg(x)$$\n",
    "\n",
    "### 幂函数\n",
    "\n",
    "$$ d(x^n) = nx^{n-1}dx$$\n",
    "\n",
    "> $$ d(x) = dx$$\n",
    "> $$ d(x^2) = 2x dx$$\n",
    "> $$ d(\\frac{1}{x}) = d(x^{-1}) = -1 \\times x^{-2}dx = -\\frac{1}{x^2}dx$$\n",
    "\n",
    "### 指数函数\n",
    "\n",
    "$$ d(a^x) = a^x \\ln a dx$$\n",
    "\n",
    "### 对数函数\n",
    "\n",
    "$$ d(\\ln x) = \\frac{1}{x}dx$$\n",
    "\n",
    "### 正弦函数\n",
    "\n",
    "$$ d(\\sin x) = \\cos x dx$$\n",
    "\n",
    "### 余弦函数\n",
    "\n",
    "$$ d(\\cos x) = -\\sin x dx$$\n",
    "\n",
    "### 正切函数\n",
    "\n",
    "$$ d(\\tan x) = \\sec^2 x dx$$\n",
    "\n",
    "### 反正弦函数\n",
    "\n",
    "$$ d(\\arcsin x) = \\frac{1}{\\sqrt{1-x^2}} dx$$\n",
    "\n",
    "### 反余弦函数\n",
    "\n",
    "$$ d(\\arccos x) = -\\frac{1}{\\sqrt{1-x^2}} dx$$\n",
    "\n",
    "### 反正切函数\n",
    "\n",
    "$$ d(\\arctan x) = \\frac{1}{1+x^2} dx$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40102f94",
   "metadata": {},
   "source": [
    "## 微分在物理学中的应用\n",
    "\n",
    "### 运动学中的微分\n",
    "\n",
    "在运动学中，微分是用来研究物体运动的变化率的。比如，在物体运动的过程中，位置的变化率可以用来描述物体的速度，速度的变化率可以用来描述物体的加速度。\n",
    "\n",
    "- 如果物体位置随着时间的变化是:\n",
    "\n",
    "\t$$ x = f(t) $$\n",
    "\n",
    "- 则位置的变化率可以用速度表示:\n",
    "\n",
    "\t$$v=\\frac{dx}{dt}$$\n",
    "\n",
    "- 速度的变化率可以用加速度表示:\n",
    "\n",
    "\t$$a=\\frac{dv}{dt}$$\n",
    "\n",
    "#### 1. 匀速直线运动\n",
    "\n",
    "- 对于匀速直线运动，位置与时间的关系：\n",
    "\n",
    "$$x=f(t)=Vt$$\n",
    "\n",
    "- 速度：\n",
    "\n",
    "$$v=\\frac{dx}{dt}=\\frac{d}{dt}f(t)=V$$\n",
    "\n",
    "- 速度的变化率可以用加速度表示，即：\n",
    "\n",
    "$$a=\\frac{dv}{dt}=\\frac{V}{dt^2}=0$$\n",
    "\n",
    "#### 2. 加速度运动\n",
    "\n",
    "- 对于加速度运动，位置与时间的关系：\n",
    "\n",
    "$$x=f(t)=\\frac{1}{2}At^2+Vt$$\n",
    "\n",
    "- 速度：\n",
    "\n",
    "$$v=\\frac{dx}{dt}=\\frac{d}{dt}f(t)=At+\\frac{dV}{dt}=At$$\n",
    "\n",
    "- 速度的变化率可以用加速度表示，即：\n",
    "\n",
    "$$a=\\frac{dv}{dt}=\\frac{dAt}{dt}=A$$\n",
    "\n",
    "#### 3. 简谐振动\n",
    "\n",
    "- 对于简谐振动，位置与时间的关系：\n",
    "\n",
    "$$x=f(t)=A\\sin(\\Omega t+\\Phi)$$\n",
    "\n",
    "- 速度：\n",
    "\n",
    "$$v=\\frac{dx}{dt}=\\frac{d}{dt}f(t)=A\\Omega\\cos(\\Omega t+\\Phi)$$\n",
    "\n",
    "- 速度的变化率可以用加速度表示，即：\n",
    "\n",
    "$$a=\\frac{dv}{dt}=\\frac{d}{dt}(A\\Omega\\cos(\\Omega t+\\Phi))=-A\\Omega^2\\sin(\\Omega t+\\Phi)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "046acc37",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x2000 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "# 解决中文乱码问题\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei'] # 设置字体为黑体\n",
    "plt.rcParams['axes.unicode_minus'] = False # 解决负号显示为方块的问题\n",
    "# 绘制图像\n",
    "def plot_f(min, max, n, f, label, color='blue', sub_plot: tuple[float, float, float] = None, title=''):\n",
    "\tx_range =np.linspace(min, max, n)\n",
    "\tif sub_plot:\n",
    "\t\tplt.subplot(*sub_plot)\n",
    "\tplt.plot(x_range, f(x_range), label=label, color=color)\n",
    "\tplt.ylabel(label)\n",
    "\tplt.legend([label])\n",
    "\tplt.xlabel('t')\n",
    "\tplt.title(title)\n",
    "\tplt.subplots_adjust(wspace=0.4, hspace=0.8)\n",
    "\n",
    "# 显示图像\n",
    "\n",
    "def show_plot(fun_name):\n",
    "\tpass\n",
    "\n",
    "\n",
    "plt.figure(figsize=(12, 20))\n",
    "\n",
    "# 静止\n",
    "plot_f(0, 10, 100, lambda x: 0*x + 3, 'x=x0', title='静止', sub_plot=(10, 3, 1))\n",
    "plot_f(0, 10, 100, lambda x: 0*x, 'v=0', title='静止', sub_plot=(10, 3, 2))\n",
    "plot_f(0, 10, 100, lambda x: 0*x, 'a=0', title='静止', sub_plot=(10, 3, 3))\n",
    "\n",
    "# 匀速直线运动\n",
    "plot_f(0, 10, 100, lambda x: 3*x, 'x=Vt', title='匀速直线运动', sub_plot=(10, 3, 4))\n",
    "plot_f(0, 10, 100, lambda x: 3+0*x, 'v=V', title='匀速直线运动', sub_plot=(10, 3, 5))\n",
    "plot_f(0, 10, 100, lambda x: 0*x, 'a=0', title='匀速直线运动', sub_plot=(10, 3, 6))\n",
    "\n",
    "g = 9.8\n",
    "# 自由落体运动\n",
    "plot_f(0, 10, 100, lambda x: 1000-g*x**2/2, 'x=1/2*gt^2', title='自由落体运动', sub_plot=(10, 3, 7))\n",
    "plot_f(0, 10, 100, lambda x: g*x, 'v=gt', title='自由落体运动', sub_plot=(10, 3, 8))\n",
    "plot_f(0, 10, 100, lambda x: 0*x + g, 'a=g', title='自由落体运动', sub_plot=(10, 3, 9))\n",
    "\n",
    "# 简谐振动\n",
    "plot_f(0, 2, 100, lambda x: np.sin(2*np.pi*x), 'x=Asin(2πt)', title='简谐振动', sub_plot=(10, 3, 10))\n",
    "plot_f(0, 2, 100, lambda x: 2*np.pi*np.cos(2*np.pi*x), 'v=2πcos(2πt)', title='简谐振动', sub_plot=(10, 3, 11))\n",
    "plot_f(0, 2, 100, lambda x: -2*np.pi*2*np.pi*np.sin(2*np.pi*x), 'a=-2π^2sin(2πt)', title='简谐振动', sub_plot=(10, 3, 12))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a555cd3",
   "metadata": {},
   "source": [
    "## 例题：求函数$f(x) = 3x$的导数：\n",
    "\n",
    "1. 首先，我们可以将$f(x)$写成$f(x) = 3x$的形式。\n",
    "2. 然后，我们可以将$f(x)$对$x$求导：\n",
    "   $$f'(x) = \\frac{d}{dx}3x = \\lim_{h\\to 0}\\frac{3(x+h)-3x}{h} = \\lim_{h\\to 0}\\frac{3h}{h} = 3$$\n",
    "3. 因此，$f'(x) = 3$。\n",
    "\n",
    "## 例题：求函数$f(x) = 3x^2 + 2x + 5$的导数：\n",
    "\n",
    "$$\n",
    "\\begin{aligned} \n",
    "f'(x) = \\lim_{h\\to 0}\\frac{f(x+h)-f(x)}{h} \n",
    "& = \\lim_{h\\to 0}\\frac{3(x+h)^2+2(x+h)+5-3x^2-2x}{h} \\\\\n",
    "& = \\lim_{h\\to 0}\\frac{3x^2+6xh+3h^2+2h+2x-2x}{h} \\\\\n",
    "& = \\lim_{h\\to 0}\\frac{6xh+3h^2+2h}{h} \\\\\n",
    "& = \\lim_{h\\to 0}\\frac{6xh+3h^2}{h} + \\lim_{h\\to 0}\\frac{2h}{h} \\\\\n",
    "& = 6x + 2 \\\\\n",
    "\\end{aligned}\n",
    "$$\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.3"
  }
 },
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